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Take a standard finite Heisenberg group with two standard generators and let's consider its growth polynomial - the polynomial which coefficients are equal to the sphere sizes. For example for $H_3(Z/...

Context: Algorithms to find short paths on Cayley graphs of (finite) groups are of some interest - see below. There can be several approaches to that task. One of ideas coming to my mind - in some ...

The Permutohedron is a remarkable convex polytope in $R^n$, such that its nodes are indexed by permutations and edges correspond to the Cayley graph of $S_n$ with respect to the standard generators, i....

Looking on the growth function for Rubik's group and symmetric group, one sees rather different behaviour: Rubik's growth in LOG scale (see MO322877): S_n n=9 growth and nice fit by normal ...

I wonder several questions about Cayley graphs of finite Heisenberg groups H3(Z/nZ). Question 1: do we know the diameter dependence on "n", at least for the standard choice of generators ? ...

Let $G$ be a perfect/ weakly perfect Cayley graph on an abelian group with respect to a symmetric generating set. In addition let the clique number be $\omega$ which divides the order of graph $n$. ...